Derivative 1/x³

  • Thread starter discy
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  • #1
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how to compute the ANTI derivative of 1 / x^3
I think I need the formula: f(x) = 1/x^n than f'(x) = -n/x^n+1 but I'm not sure and don't know how to use it.

I know the answer is: -0.5 * x^-2 but have no idea why.

could someone explain this to me please?
 

Answers and Replies

  • #2
LCKurtz
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The familiar antiderivative formula

[tex]\int x^n\, dx = \frac{x^{n+1}}{n+1}+C[/tex]

also works for negative exponents. Write your fraction as a negative exponent.
 
  • #3
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The familiar antiderivative formula

[tex]\int x^n\, dx = \frac{x^{n+1}}{n+1}+C[/tex]

also works for negative exponents. Write your fraction as a negative exponent.

thanks for your answer.

now how would I put 1/x³ into that formula to get -0.5 * x^-2 ?
 
  • #4
LCKurtz
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thanks for your answer.

now how would I put 1/x³ into that formula to get -0.5 * x^-2 ?

Write 1/x³ as xn using a negative exponent and use the formua.
 
  • #5
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hm okay. like x^-3. got it.

I guess I should learn this formula, not only because it's a "familiar" one for you guys. But also because for some reason it's not on my formula sheet.

:) tnx for your help.
 
  • #6
SteamKing
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